Dynamic limit equilibrium analysis of sliding block for rock slope based on nonlinear FEM

Traditional rigid body limit equilibrium method (RBLEM) was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the structure, while the strength reduction method relies on the arbitrary decision on the failure criteria. The dynamic limit equilibrium solution was proposed for the stability analysis of sliding block based on 3-D multi-grid method, by incorporating implicit stepping integration FEM. There are two independent meshes created in the analysis: One original 3-D FEM mesh is for the simulation of target structure and provides the stress time-history, while the other surface grid is for the simulation of sliding surface and could be selected and designed freely. As long as the stress time-history of the geotechnical structure under earthquake scenario is obtained based on 3-D nonlinear dynamic FEM analysis, the time-history of the force on sliding surface could be derived by projecting the stress time-history from 3-D FEM mesh to surface grid. After that, the safety factor time-history of the sliding block will be determined through applying limit equilibrium method. With those information in place, the structure's aseismatic stability can be further studied. The above theory and method were also applied to the aseismatic stability analysis of Dagangshan arch dam's right bank high slope and compared with the the result generated by Quasi-static method. The comparative analysis reveals that the method not only raises the FEM's capability in accurate simulation of complicated geologic structure, but also increases the flexibility and comprehensiveness of limit equilibrium method. This method is reliable and recommended for further application in other real geotechnical engineering.

基于FEM-DFN的页岩气储层水力压裂复杂裂缝交错扩展模型

页岩气藏压裂过程中,常遇到因施工压力超限储层压不开、近井地带裂缝形态复杂而引起砂堵的恶性事故,如何有效模拟复杂裂缝的起裂与交错扩展形态是页岩气体积压裂优化设计的关键。为此,基于有限元—离散裂缝网络(FEM-DFN),考虑水力裂缝扩展的非线性损伤破裂力学行为与裂缝面摩擦效应,改进了拉伸—剪切复合破裂模式的本构方程,建立了基于显式时间积分的页岩气储层水力压裂复杂裂缝交错扩展的多场耦合模型,并在实验室和现场微地震监测中进行了验证。研究结果表明:①水力裂缝与天然裂缝交错机制主要为2类,即被天然裂缝诱导并沿天然裂缝扩展、直接穿透天然裂缝,地质与工程因素对交错机制的转变存在阈值,当排量超过26 m^(3)/min时,或压裂液黏度超过40mPa·s时,或应力差超过18MPa时,或裂缝面摩擦系数超过0.8时,水力裂缝将直接穿透天然裂缝;②天然裂缝对水力裂缝的诱导作用随着两者夹角的变化而变化,在夹角较小的情况下,水力裂缝容易在最大水平主应力方向交汇点之前提前被天然裂缝诱导,而当夹角增大时则在交汇点处进入天然裂缝扩展,且表现为一侧拉张裂缝一侧剪切裂缝;③相邻两簇水力裂缝容易在天然裂缝的诱导作用下相互吸引,进而交汇成优势主裂缝。结论认为,天然裂缝的分布状态是决定压裂裂缝复杂度的关键性因素,研究成果可为中深层页岩气压裂裂缝分析和施工参数优化提供理论与技术支撑。

基于FEM的超高压液压顶升装置力学特性分析

液压顶升装置各部件在超高压下的力学特性是影响其性能的主要因素,也是超高压技术的难题。采用有限元方法研究超高压液压顶升装置各部件的材料、内径、厚度等不同时,其液压系统刚度、模态、固有频率、位移、应力的变化规律。有限元计算结果与压力试验结果较为接近,验证了有限元模型及边界条件的有效性。结果表明:液压弹簧刚度随液压缸内径增大而增加、随振幅增加而下降,其影响随内径增加而减少;系统前3阶固有频率随地面强度增大而增加;Bonded工况极限应力值最小,Frictionless工况极限应力最大,极限应力随地面强度增加而减少;C20地面时,最大位移随摩擦因数增加而增加,最大应力随地面强度增加而增加;C30地面时,最大位移随摩擦因数增大先增后减,其位移、应力临界摩擦值分别为0.43、0.59;结构钢地面时,极限位移显著减少。液压缸同长度不同位置极限位移差值随地面强度而增加;液压缸底端应力值随地面强度增加而增加;液压缸外表面一孔侧位移均小于二孔侧,且极限位移更靠近顶端,并交替出现极值。分析了超高压液压装置的应力-应变过程,为其结构设计、密封设计及使用提供了参考。

Analysis of a Gyroscope′s Rotor Nonlinear Supported Magnetic Field Based on the B-Spline Wavelet-FEM

A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.

五强溪水电厂底孔密封性能仿真模拟研究

针对水电站闸门水封存在密封性能在运行过程中裂化、密封性能预测困难、水封更换时螺栓预紧量的确定缺乏理论依据等问题,提出基于多元线性回归的螺栓预紧量补偿模型。结合工程实例,通过Ogden公式建立方头P型水封橡胶超弹性本构模型,建立复杂工况下水封密封结构非线性有限元计算模型。基于Ansys计算了4种影响因素下的水封接触应力,分析了多种影响因素与水封密封性能之间的独立影响和综合影响规律,在有限元分析的基础上,基于多元线性回归建立了接触应力计算公式,构建了螺栓预紧量补偿模型,实现了水封密封性能反演和螺栓预紧量补偿计算。结果表明,基于螺栓预紧量补偿模型得到的接触应力与预期值的平均相对误差为7.6%,最大相对误差为16.9%,模型能够实现在水封安装工况改变时对螺栓预紧量进行修正,从而得到预期水封密封性能,为实际工程中水封结构的设计、安装提供了可靠依据。

土体强度折减对海上升压站结构抗震设计的影响

通过有限元非线性时程分析,对比API规范法与考虑土体强度折减作用后某海上升压站桩基及上部平台结构的水平向应力与变形等主要设计指标,结果表明,考虑土体强度折减后,土体对于桩基的水平向约束力减弱,单桩的变形与受力均出现大幅增加,且上部结构的整体水平运动特征更为显著,使用API规范计算上部平台结构的应力结果偏保守,建议在海上升压站的桩基础设计时根据场地土的特性选取土体强度折减模型并着重校核桩基础的关键设计指标。

多柔性体系统动力学的有限元方法(MUFEM)

本文探讨多柔性体系统动力学的一种新的数值仿真方法一多体有限元方法（MultibodyFiniteElementMethod，MUFEM）。MUFEM以有限元方法为基础，综合区域分解法（DDM）和非连续体变形分析方法（DDA）的主要优点。MUFEM的主要特点是：1）构造边界网格描述系统动态变化的拓扑几何关系；2）采用FEM模型和类似子结构的方法分析多柔性体系统的动力学特性；3）各子块之间可能接触边界的非连续性用Lagrange乘子处理；4）摩擦接触问题用非线性数学规划方法求解。算例表明，MUFEM能很好模拟多柔性体系统的运动以及相互之间的作用，有良好的发展前景。

混凝土重力坝整体结构安全评价

为了突破当前重力坝评价体系中只着眼于独立坝段而忽略整体作用的趋势,以国外某工程中的混凝土重力坝为例,建立重力坝全坝段有限元分析模型。考虑混凝土材料、地基岩体的动力非线性特性,采用接触非线性单元模拟不同坝段之间的横缝状态;通过对不同坝段坝体的位移、应力的计算和分析,研究坝体在不同荷载工况下的静动力响应、屈服特性与破坏模式,对重力坝全坝段的安全性能作出整体评价。研究采用的评价方法成果合理有效。

基于CFD-FEM的浮式结构水弹性响应数值模拟

开发并验证了一种基于CFD-FEM耦合的弹性浮体水弹性响应计算模拟方法。采用CFD方法建立黏性数值水池模拟非线性波浪,弹性浮板进行有限元离散,并在交界面进行数据交互实现耦合计算;通过与水池试验数据和三维板理论在各种波浪环境下的浮体垂向位移结果对比,证实CFD-FEM耦合方法的有效性。并进一步研究了浮板的厚度、入射波波幅和浮板的三维效应对浮板水弹性响应的影响。结论表明,波幅的增加会加剧弹性浮板的水弹性响应,浮板各点处的垂向位移随波幅的增加而增大;当浮板厚度改变时,不同厚度浮板自由端处的垂向位移差异较小,而在中部等位置处,厚度对浮板的水弹性响应有较大的影响。

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

基于Java的OOFEM框架模型研究

面向对象的有限元(OOFEM)通用框架的构造对于有限元算法和并行有限元的研究具有重要意义。该文利用Java和面向对象技术,初步实现了这种非线性有限元框架模型,并且对其理论基础、功能构造、类库实现和算法设计等进行了研究。算例表明:数值结果与理论值是吻合的,框架模型是正确的和可靠的。

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

椭圆波导FEM放大器的非线性特性研究

以椭圆波导、平板摇摆器为 FEM放大器的模型 ,导出了自洽的注波互作用三维非线性方程组。在此基础上编制了相应的程序。利用该程序分析了 FEM放大器的饱和功率、效率以及带宽等高频特性。考虑了摇摆器渐变、空间电荷波、电子初始速度零散对高频特性的影响。

Evaluation of the Impact of Truck Overloading on Flexible Compacted Gravel Lateritic Soil’s Pavements by FEM with Cast3M^©

Within the framework of a FEM of the nonlinear behavior of lateritic pavement of Senegal, the effect of truck overloading is studied to estimate its impact on the deformability of road pavement on compacted gravel lateritic soils. For that purpose, various loading conditions were tested to measure the impact on the critical response parameters of road pavement design. The implementation of the models was realized with Cast3M©. This study allowed us to point out that the observed variations are linear and would help to plan in advance the impact of axle overloads for a better evaluation within the framework of the mechanistic (M. E.) design of pavements.

A New Pursuit Mode of Nonlinear Wave Surface

The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. And the basis for establishing the numerical mode of nonlinear wave in time domain is to trace the position of wave free surface and to calculate the instantaneous surface height and surface potential function. This paper firstly utilizes the ‘0-1' combined BEM to separate the boundary by means of discretization of Green's integral equation based on the Laplace equation, then separates the free surface of wave with FEM and derives the FEM equation of wave surface that satisfies the nonlinear boundary conditions. By jointly solving the above BEM and FEM equations, the wave potential and surface height could be obtained with iteration in time domain. Thus a new kind of nonlinear numerical mode is established for calculating wave transformation. The wave test in the numerical wave tank shows that the numerical simulation with this mode is of high accuracy.

基于CFD−非线性有限元双向耦合的集装箱船波浪下结构崩溃数值仿真

[目的]充分考虑载荷非线性和物面非线性因素的影响,研究集装箱船在波浪下结构响应及动态结构崩溃模式。[方法]首先,基于CFD平台建立船舶水动力模型,采用重叠网格法实现船体水动力模型动边界网格与远场流体域的欧拉网格间的匹配,在流体全域内采用流体体积法模拟自由面非线性,在流场全域内求解三维N–S方程,实时求解非线性波浪载荷;然后,建立可模拟船舯崩溃行为的船舶非线性有限元模型,基于显式动力学非线性有限元法计算包含塑性和屈曲的时域崩溃响应;最后,实现水动力模型与结构有限元模型在湿表面上的流体压力和节点位移的传递,以此进行CFD求解器与非线性有限元求解器间的双向迭代耦合,并实时计算4600 TEU集装箱船结构崩溃过程中的非线性波浪载荷和结构崩溃响应。[结果]结果显示,在极端波浪下上部至中部结构广泛进入塑性状态,主甲板、舷侧板、甲板纵骨和舷侧纵骨等构件在波浪下出现明显的屈服及失稳,甲板纵骨和舷侧纵骨等骨材发生严重的侧向失稳,船体结构丧失了承载能力。[结论]所提方法可较准确求解结构响应及动态崩溃模式,可作为研究船舶结构崩溃响应的一种新方法。

A Coupling Model of Nonlinear Wave and Sandy Seabed Dynamic Interaction

In the paper, a weak coupling numerical model is developed for the study of the nonlinear dynamic interaction between water waves and permeable sandy seabed. The wave field solveris based on the VOF （Volume of Fluid） method for continuity equation and the two-dimensional Reynolds Averaged Navier Stokes （RANS） equations with a k-ε closure. The free surface of cnoidal wave is traced through the PLIC-VOF （P/ecewise Linear/nterface Construction）. Blot＇s equations have been applied to solve the sandy seabed, and the u-p fmite dement formulations are derived by the application of the Galerkin weighted-residual procedure. The continuity of the pressure on the interface between fluid and porous medium domains is considered. Laboratory tests were performed to verify the proposed numerical model, and it is shown that the pore-water pressures and the wave heights computed by the VOF-FEM models are in good agreement with the experimental results. It is found that the proposed model is effective in predicting the seabed-nonlinear wave interaction and is able to handle the wave-breakwater-seabed interaction problem.

Numerical Investigations on Transient Behaviours of Two 3-D Freely Floating Structures by Using a Fully Nonlinear Method

在靠近的最近的二漂浮结构很通常在近海的设计被看见。他们经常受到陡峭的波浪并且因此，他们的水动力学特征上的短暂效果担心大。这份报纸使用伪任意的 Lagrangian-Eulerian 有限元素方法(QALE女性)基于充分非线性的潜在的理论( FNPT )，组织自由( DOF )的度数字地调查在二 3-D 漂浮之间的相互作用，它与 6 经历运动，并且与不同事件角度受到波浪。漂浮的结构，伴随的结构的效果，和运动和波浪上的非线性的短暂行为结构上的负担是学习的主要焦点。调查揭示一引起更加更大的结构的重要短暂效果处于稳定的状态比那打手势。结果也显示在靠近的最近的伴随的结构在引起第二顺序部件具有到基本的类似的意义的更强壮的非线性提高在不同运动模式和结果之间的相互作用。

An Improved Numerical Simulation Mode of Nonlinear Wave with Consideration of High Order Terms

SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.